In this thesis, a strategy for phasor measurement unit (PMU) optimal placement and signal selection is proposed for monitoring critical oscillations in electric power systems. A robust indicator, mode in output proportion factor (MOPF), is introduced for identify critical PMU locations and signal channels, in order to better monitor power system oscillations with specific oscillation modes. Based on the proposed MOPF, a two-layer algorithm is presented. This algorithm could benefit system operators and planners in the following two ways: 1) it identifies existing PMU devices and signal channels, which provides the best observability for critical oscillation modes; 2) it suggests optimal locations for further PMU deployments, in order to enhance the observability for critical oscillation modes. The performance of proposed algorithm is illustrated via a modified 16-machine-68-bus system and NPCC-140-bus system. Based on the proposed algorithm, all modes of interest can be observed sufficiently under various disturbances. Therefore, the proposed algorithm can be applied to prioritize or deploy PMUs to observe critical oscillation modes in power systems.